Weight is defined as the force of gravity on an object. We can use Newton's second law to write an equation for weight.

If the ball weighs  on Earth, then its mass can be found using this equation and the acceleration of gravity on Earth.

Use this mass and the given weight on the new planet to find the acceleration of gravity on this new planet. Though our initial values (and thus our final values) only allow one significant figure, we will not round until the end of all calculations. This ensures that we preserve accuracy before adjusting for precision.

Adjust this value to one significant figure by rounding up. The zero in the tens place is before the decimal, and is not considered significant.

We must use Newton's law of universal gravitation to solve this question.

There are three variables that really change the force of gravity: the mass of each object and the distance between the bodies.

The important thing to recognize here, though, is that when an object is in the center of the earth, the mass of the earth is distributed symmetrically all around it. It's like being in the center of a giant bubble. Because the mass is symmetrically distributed, the mass that is trying to pull the object in each direction is equal. Essentially, the mass pulling upward cancels out the mass pulling downward, and the mass pulling right cancels out the mass pulling left.

This happens for the entirety of the circle, leaving you with a net force of zero acting upon the object.

For this problem, we are comparing the force of gravity on the surface, or weight, to the force of gravity on the satellite. We can use Newton's second law to find the weight of the satellite, and the law of universal gravitation to find the gravity on the satellite. These two terms will be equal to one another.

Let's call  the Earth and  the mass of the satellite.

Notice that the masses of the satellite cancel out.

This formula gives us the acceleration of gravity in terms of the mass of the Earth and the distance from the Earth's center. We can write two separate equations, one for the surface and one for the satellite. Since the mass of the Earth doesn't change and  is a constant, the only variable that can change is , the distance between the objects.

On Earth,  is the radius of the earth. For the satellite,  is the radius of the Earth PLUS the orbiting distance; therefore . Because we are dividing by our , a greater  gives us a smaller .

The satellite in space will have a smaller acceleration due to gravity. It will not be zero, but it will be smaller than the acceleration on the surface.

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleretion. Remember that weight is equal to the mass times acceleration due to gravity.

Set our two forces equal and solve for the acceleration.

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleretion. Remember that weight is equal to the mass times acceleration due to gravity.

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Set our two forces equal and solve for the acceleration.

The formula for force is given by Newton's second law:

Both rocks will experience the same acceleration, , or the acceleration due to gravity.

Use the mass of each rock in this equation to find which rock experiences a greater force.

We can see that the force on the rock with mass of is equal to three times for the force on the rock with mass of . The heavier rock experiences the greater force.

Even though the rocks have different masses, the acceleration on both will be , the acceleration due to gravity. We can look at Newton's second law to see the force experienced by the rocks:

When objects are in free-fall, the acceleration will be equal to the acceleration from gravity, regardless of the mass of the object.

Newton's second law states:

In this case the acceleration will be the constant acceleration due to gravity on Earth.

Use the acceleration of gravity and the mass of the ball to solve for the force on the ball.

The answer is negative because the force is directed downward. Since gravity is always acting downward, a force due to gravity will always be negative.

First we need to find the mass of the astronaut using Newton's second law.

We know the total weight of the astronaut and the acceleration due to gravity on Earth, allowing us to solve for her mass.

Now that we know her mass, we can look at her weight on the distant moon. We know her weight and mass, allowing us to solve for the acceleration due to gravity in this new environment.

Newton's second law states that:

We know from the problem that the acceleration due to gravity on the moon is less than the acceleration due to gravity on Earth. The mass of the object, however, will remain constant. The result is that the force of gravity on the object while on the moon will be less than the force on the object while on Earth.

This means that the weight of the object while on the moon must be less than . Since the object has a weight on Earth, however, we know that its weight on the moon cannot be zero. This would imply that either the acceleration due to gravity on the moon is zero, or that the mass is zero, neither of which is possible. This allows us to eliminate from the answers.

The only other option that is less than is .